Ergodic Theory and Dynamical Systems

Research Article

Dynamics of entire functions near the essential singularity

Robert L. Devaneya1 and Folkert Tangermana1

a1 Department of Mathematics, Boston University, Boston, Mass. 02215, USA

Abstract

We show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

(Received December 04 1985)